Data Structures for Halfplane Proximity Queries and Incremental Voronoi Diagrams

We consider preprocessing a set $S$ of $n$ points in convex position in the plane into a data structure supporting queries of the following form: given a point $q$ and a directed line $\ell$ in the plane, report the point of $S$ that is farthest from (or, alternatively, nearest to) the point $q$ among all points to the left of line $\ell$. We present two data structures for this problem. The first data structure uses $O(n^{1+\varepsilon})$ space and preprocessing time, and answers queries in $O(2^{1/\varepsilon} \log n)$ time, for any $0 < \varepsilon < 1$. The second data structure uses $O(n \log^3 n)$ space and polynomial preprocessing time, and answers queries in $O(\log n)$ time. These are the first solutions to the problem with $O(\log n)$ query time and $o(n^2)$ space. The second data structure uses a new representation of nearest- and farthest-point Voronoi diagrams of points in convex position. This representation supports the insertion of new points in clockwise order using only $O(\log n)$ amortized pointer changes, in addition to $O(\log n)$-time point-location queries, even though every such update may make $\Theta(n)$ combinatorial changes to the Voronoi diagram. This data structure is the first demonstration that deterministically and incrementally constructed Voronoi diagrams can be maintained in $o(n)$ amortized pointer changes per operation while keeping $O(\log n)$-time point-location queries.Comment: 17 pages, 6 figures. Various small improvements. To appear in Algorithmic

Continuous Blooming of Convex Polyhedra

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.Comment: 13 pages, 6 figure

Worst-Case Optimal Tree Layout in External Memory

Consider laying out a fixed-topology binary tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the optimal number of memory transfers is Θ([D over lg(1+B))] when D = O(lgN), Θ([lgN over lg(1+[BlgN over D])]) when D=Ω(lgN) and D=O(BlgN), Θ([D over B]) ,when D=Ω(BlgN).National Science Foundation (U.S.) (Grant CCF-0430849)National Science Foundation (U.S.) (Grant OISE-0334653

Meshes Preserving Minimum Feature Size

The minimum feature size of a planar straight-line graph is the minimum distance between a vertex and a nonincident edge. When such a graph is partitioned into a mesh, the degradation is the ratio of original to final minimum feature size. For an n-vertex input, we give a triangulation (meshing) algorithm that limits degradation to only a constant factor, as long as Steiner points are allowed on the sides of triangles. If such Steiner points are not allowed, our algorithm realizes \ensuremathO(lgn) degradation. This addresses a 14-year-old open problem by Bern, Dobkin, and Eppstein

Plio-Pleistocene geological evolution of the northern Sicily continental margin (southern Tyrrhenian Sea): new insights from high-resolution, multi-electrode sparker profiles

High-resolution seismic profiles were acquired in the north Sicily offshore region with an innovative, multi-tip sparker array which lacks ringing and has a base frequency around 600 Hz. The new data, combined with published data, suggest that intra-slope and extensional basins formed as a consequence of the late Miocene (?)–early Pliocene shortening and thrusting, and the middle (?)–late Pliocene continental rifting affecting the internal side of the Sicilian-Maghrebian chain. Early (?) Pleistocene to Holocene high-amplitude and high-frequency sea-level changes resulted in repeated sub-aerial exposure and flooding of the shelf, and the deposition of cyclically arranged hemipelagic and shelf sediments. An uplift of the shelf could explain the non-preservation of the transgressive and of the lowstand wedge systems tracts in the oldest sequences

Food intolerance and chronic constipation: manometry and histology study.

BACKGROUND: Chronic constipation in children can be caused by cows' milk intolerance (CMI), but its pathogenesis is unknown. AIMS: To evaluate the histology and manometry pattern in patients with food intolerance-related constipation. PATIENTS AND METHODS: Thirty-six consecutive children with chronic constipation were enrolled. All underwent an elimination diet and successive double-blind food challenge. All underwent rectal biopsy and anorectal manometry. RESULTS: A total of 14 patients were found to be suffering from CMI and three from multiple food intolerance. They had a normal stool frequency on elimination diet, whereas constipation recurred on food challenge. The patients with food intolerance showed a significantly higher frequency of erosions of the mucosa, and the number of intra-epithelial lymphocytes and eosinophils. The rectal mucous gel layer showed that the food-intolerant patients had a significantly lower thickness of mucus than the other subjects studied. Manometry showed a higher anal sphincter resting pressure and a lower critical volume in food intolerance patients than in the others suffering from constipation unrelated to food intolerance. Both histology and manometry abnormalities disappeared on the elimination diet. CONCLUSIONS: Food intolerance-related constipation is characterized by proctitis. Increased anal resting pressure and a reduced mucous gel layer can be considered to be contributory factors in the pathogenesis of constipation